Download Finish Angle Action Example - Lecture Notes | PHYS 5210 and more Study notes Physics in PDF only on Docsity! Lecture. 23.
Method:
For euch. coord, calentete
Tavert te_get E(T,+)
| Thea OSes
Looking et Kepler problem
< : ee i
Bt ~ tm dm Ps Te
Py =. LQ = sanst
Pr = + mE + ae
Jy: SL Mb= 22
§ +) ake
Worked out
Te
integral:
I
Ugh
[Fi nish action - ensle erenele. a
een Fires Uy?
> (T2yyV
= eons tent Moe separ cSle \ _
de
OTe
T+ on (PEP - 29)
rs
|Get Ely: The an J - 27%
Tp rtge 2d
—— “Sree
{3-223 vv
TThe« Fregrencies _are
oon BE 3zah we yt
bog BTA fe ty
}-
[é press iin
4 f
NeF neh
Ale neles corstent
Je Ny 2 Lategetl
Note! Boke s. origins acento the ory saich
to - to guentigeg eetion |
| Hece do get correct enetsy levels Tor b
er i
— Mr ane es
: ee ‘ Fe
Bee : E = = AWer ney = o> Ww
iReut desenccocy * celction Setweer
Eo
no nt eye,
int gig ht
yelropen :
qa.
Gert... Crap by from
General soletion will Se super portion of meter
net
| Sey ule \.2 fe).
DE >
at (xo) * ale \
Then
. | \ Pn &) Lte\ why = 2 an J Pale pale) rly
-S..
So me SPL LO @ etx
Alse
y= 2 6.6) 2, b,
bekich give, Sat Bm Spal) 500). che
Explie+ generel seletyon
Bet lees fraise some. questie as
)
>Does i-Mate. secies for un converge *
- - 4s >
Do 2 herivetives COMmVElge s
- Bo series for fa 5 converge to actual £ 752)
1 ~ Cen we apely this osethed te moce aenecal
Sticy egy Teoh), re rle)?.
23,3
: . = dz OE RRR L TO ntet sn ET a
| tafe th = 2 dee Sin F Jla. cos a thos DJ
£05 2 dae on sine =. Zan pals)
LOU eclelics® “fhese. aprestions
One osiche i
_wMey beve seen thet sole
er to AD weve ean.
Sen also Ge exptessel
nls, t) = f lxrety + U(ye~et)
Rother Arfecent from bet we fonnch
Text G39 reconciles cstetert ng.
But FD usent to ctelle aboett hors metho gene relae! |
Genel stein an
Gerecelize ce $4 wose t
Sey the steics moves in externa! potenial | os
Vos Js &) dx ——_|
Extre cesteriny Force fait leagth 2-U lx) woe) |
1 mee & Ind S Pfings pullies
, r a t
is Idea to tecsier
Not very likely bet prdth 15 unsefal foc ather
sitactions
pope oo RL Sate
Eqn of wetted aylz.e J~vG@u =v.
Be. 4
ht cece OEY TL A ..
{
| too de~
_|So ile) +t UP FF awe
_. eq action
| . 5
[Exe ple: co _— ee
ef el OT, Te co ast, est ge OO Hen menie oseilletor
| a wo
Pb) Ge DK OM EK LL ms cont.
ne —/—.-> > . .
© [fap Ss Spies po.
| ~ x pl p-* eps cox
pe xe +f. w'xtw ant) p= O.
Sve welt VE xt
2 dea
ap BOS KE) 4 rx Pp. Zeuy P
(i- e xp! ot. Lo lps 0
“ Legeadire’s agus!
coletion CP (x)
Q
= (04)
7
_. Very general. Since Cur = arb fens of x
ft . Bessels_ equetion solitions. Sn (cox) , No
23.4
. tb Again leak foe soliton _ tale Ad? po cos (eat + B ae
tox)
